Because individual biomolecules are very small, x-ray scattering experiments usually determine their structures by an analysis of scattering from a large number of them. In crystallography, scattering by many molecules in identical orientations vastly enhances the signal from a single molecule. However, not all biomolecules form crystals. They are more usually found in disordered ensembles in aqueous solutions or in biomembranes. Now, researchers from Arizona State University, SLAC National Accelerator Center, Berkeley Lab, Brookhaven National Laboratory, and the University of Wisconsin-Milwaukee have performed, at ALS Beamline 9.0.1, the first experimental demonstration of a method that amplifies the information in the x-rays that scatter from disordered biomolecules, allowing the reconstruction of an image of a single molecule from fluctuations in the scattering from an ensemble of randomly oriented copies.

Out of Many, One Image

E pluribus unum ("out of many, one") is a famous national motto that captures the essence of the innovation in x-ray imaging achieved by Saldin et al., reported here. The researchers confirmed a 1977 suggestion by Zvi Kam that, despite the "noise" caused by x-rays scattering off of multiple randomly oriented copies of an object, it's possible to reconstruct an image of a single copy by analyzing and correlating the subtle patterns hidden in the noise. The process is akin to reconstructing an image of a grain of sand by detecting the ripples created by a pinch of sand grains tossed into a stormy ocean. The ripple "signal" from a single grain of sand would be hopelessly lost, but with many grains, a characteristic, repeating wave pattern can be detected, while the meaningless noise is discarded. The results represent one more important step in the steady progress that has been made in the development of a "lensless" x-ray technique to study micro- and nanoscale objects such as proteins, viruses, and biological cells in three dimensions. For related work done at the ALS, see the following highlights: "Demonstration of Coherent X-Ray Diffraction" (2004), "Biological Imaging by Soft X-Ray Diffraction Microscopy" (2005), and "Lensless Imaging of Whole Biological Cells with Soft X-Rays" (2010).

The overwhelming majority of known molecular structures at the atomic scale have been determined by x-ray crystallography, a technique that cannot be applied to molecules that resist crystallization (e.g., many membrane proteins). One solution to this problem would be to exploit the billionfold increase in peak brightness provided by an x-ray free-electron laser, due to which it may be possible to detect meaningful signals from single microscopic particles. Because of the large flux of radiation, however, it is necessary to work in the so-called "diffract and destroy" mode, in which the x-ray pulse must terminate within about 50 fs to avoid resolution-limiting effects resulting from the disintegration of the particle. The difficulty of targeting a single particle in such an experiment could be overcome with the development of a method for extracting structural information from scattering by a disordered ensemble of particles.

The absence of periodicity in such a sample means that the scattered x-rays form a continuous distribution, as opposed to discrete Bragg peaks. This allows for analysis of the data at a finer sampling rate, both radially (outward from the center) as well as angularly (around a ring of constant radius). If sampled finely enough, it has been suggested that enough information to reconstruct an image may be obtained from minute fluctuations in the angular intensities. These fluctuations can be detected via autocorrelation: a statistical analysis that facilitates the extraction of subtle patterns from a noisy signal. Since angular autocorrelations do not depend on a particle's orientation, it can be shown that the sum of the angular correlation functions from many diffraction patterns (each from many particles) converges to that from one particle. This can then be inverted to an image of a typical particle using iterative phasing methods.

In these experiments, the particles were nanorods varying in length and diameter by approximately 10% to 15% in both dimensions; a small but significant fraction (~20%) of the nanoparticles were spherical in shape. The sizes of the nanoparticles were approximately that of a typical virus, suggesting a possible application to determining the structures of virus particles supported on a similar substrate. The researchers collected soft x-ray transmission diffraction patterns using 750-eV highly coherent x-rays (1.65 nm in wavelength). Hundreds of diffraction patterns were collected from different 15-micron-diameter regions, each containing approximately 10 ± 5 nanorods. The experiments also showed that, even if the measured diffraction patterns are from two different particle shapes (in this case a nanorod and a nanosphere), simultaneous reconstruction of the real-space structures of the both particle types is possible.

Left: Reconstruction of a single nanorod/nanosphere diffraction pattern from the average angular autocorrelations of the measured diffraction patterns. Right: Real-space image of a superposed nanorod/nanosphere reconstructed from the diffraction pattern on the left.

As demonstrated for the first time in these experiments, the advantages of signal amplification, damage reduction, and access to oversampled intensities may be combined to determine the structure of a single particle by diffraction patterns from many identical particles with neither translational nor orientational order. The extra information present in the angular correlations allows for an ab initio reconstruction, free of modeling and a priori assumptions.